An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 8، 1 (WINTER) - شماره پیاپی 29، فروردین 2018، صفحه 29-38   

نوع مقاله: Review Article

نویسندگان

Driss Sbibih^{* 1}؛ Bachir Belkhatir²

¹Department of Mathematics, Faculty of Sciences, University Mohammed First

²LANO Laboratory, University Mohammed First, Oujda, Morocco

چکیده

In this paper, we study a geometric G^2 Hermite interpolation by planar rational
cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures
interpolated per each rational segment. We give the necessary and the sufficient
intrinsic geometric conditions for two C^2 parametric curves to be connected with G2
continuity. Locally, the free parameters within a rational cubic Bézier curve should
be determined by minimizing a maximum error. We finish by proving and justifying
the efficiently of the approaching method with some comparative numerical and
graphical examples.

کلیدواژه‌ها

Hermite interpolation؛ Rational curve؛ G^2 continuity؛ Geometric conditions؛ Optimization